Gravity escapes. But I’ve been wondering about that, too. Magnetic field lines: Can they escape? If not, then what’s the big problem here; if magnetic field lines can’t escape, then we shouldn’t be surprised that the magnetic field of a black hole is wimpy, right? But then, I’m not a physicist, as should be obvious to any such person reading about my total state of confusion!
According to General Relativity gravity is a curvature of spacetime so it has nothing to escape. It’s simply there.
You may be thinking about particle creation at the black hole horizon when an anti-particle is launched outside the hole. The significance has to do with whether or not information can escape a black hole.
You’re saying gravity escapes gravity. Are you sure you want to go on record with that? And gravity doesn’t affect magnetic fields. But magnetism affects measurements of gravity (a little).